Hey can anyone please help me with this.
Find the probability range that a random sample of size $4$ from $U(0,1)$ is less than $\frac{1}{2}$.
I.e find $P\left(y_4-y_1<\frac{1}{2}\right)$ where $y$ is the $n^{th}$ order statistic.
The way this is approached is first get the joint distribution, then do the bivariate transformation and finally integrate. I have the solution but I am unable to understand how the bivariate bounds are reached as shown in image 2. please help
